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C. k-Tree

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputQuite recently a creative student Lesha had a lecture on trees. After the lecture Lesha was inspired and came up with the tree of his own which he called a *k*-tree.

A *k*-tree is an infinite rooted tree where:

- each vertex has exactly
*k*children; - each edge has some weight;
- if we look at the edges that goes from some vertex to its children (exactly
*k*edges), then their weights will equal 1, 2, 3, ...,*k*.

The picture below shows a part of a 3-tree.

Help Dima find an answer to his question. As the number of ways can be rather large, print it modulo 1000000007 (10^{9} + 7).

Input

A single line contains three space-separated integers: *n*, *k* and *d* (1 ≤ *n*, *k* ≤ 100; 1 ≤ *d* ≤ *k*).

Output

Print a single integer — the answer to the problem modulo 1000000007 (10^{9} + 7).

Examples

Input

3 3 2

Output

3

Input

3 3 3

Output

1

Input

4 3 2

Output

6

Input

4 5 2

Output

7

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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